Existence and Uniqueness Solution of Certain Integral Equation

Authors

  • Honer Naif Abdullah Department of Mathematics, College of Basic Education, Duhok University, Kurdistan Region – Iraq

DOI:

https://doi.org/10.25007/ajnu.v12n4a1978

Abstract

The aim of this work is to study the existence and uniqueness of solutions of certain integral equations by using the Picard approximation method and Banach fixed point theorem. The study of integral equations is more general and leads us to improve and extend some results of Butris.

Downloads

Download data is not yet available.

References

Butris, R. N. , (1984), Solutions of Volterra integral equations of second kind, Thesis, university of Mosul, College of Science, Iraq.

Coddington, E. A. and Levinson, N., (1955), Theory of ordinary differential equations, Mc Graw-Hill Book Company, New York.

Golberg, M. A., (1978), Solution methods for integral equations theory and application, Nevada Las Vegas University, Nevada Plenum press, New York and London.

Guoqiang, H. and Ruifang, W., (2001), The extrapolation method for two-dimensional Volterra integral equations based on the asymptotic expansion of iterated galerkin solutions, Journal of and Applications,Vol.13, No. 1, Spring. Integral Equations

Hendi, F. A. and Al-Hazm, Sh., (2010), The non-linear Volterra integral equation with weakly kernels and toeplitz matrix method, Vol. 3, No.2.

Hochstadt, H., (1973), Integral Equations, John Wiley and Sons, New York.

Jaswon, M. A. and Symm, G. T., (1977), Integral Equations Methods in Potential Theory and Jovanovich Publishers, Academic press, London. Elastostatics, A subsidiary of Hart court brace

Jeffery, A. and Chambers, LI. G., (1976), Integral Equations, A short Course, International Textbook Company Limited.

Krasnov, M., Kiselev, A. and Makarenko, G., (1971), Problems and Exercises in Integral Equations, Mir Publishers, Moscow.

Maleknejad, K. and Alizadeh, M., (2009), Volterra type integral equation by the Whittaker cardinal expansion, The Open Cybernetics and Systemic Journal, Vol. 3, pp. 1-4.

Mikhailov, L. G., (1970), A New Class of Singular Integral Equations, Akademic-Verlag, Berlin.

Parton, V. Z. and Perlin, P. I., (1982), Integral Equations in Elasticity, Mir Publishers, Moscow.

Rama, M. M., (1981), Ordinary Differential Equations Theory and Applications, Britain.

Royden, H. L., (2005), Real Analysis, Prentice-Hall of India Private Limited, New Delhi-110 001.

Shestopalov, Y. V. and Smirnov, Y. G., (2002), Integral Equations, Karlstad University.

Struble, R. A., (1962), Non-Linear differential equations, Mc Graw- Hall Book Company Inc., New York.

Tarang, M., (2004), Stability of the spline collocation method for Volterra integro-differential equations, Thesis, University of Tartu.

Tricomi, F. G., (1965), Integral equations, Turin University, Turin, Italy, June.

Published

2023-09-19

How to Cite

Naif Abdullah, H. (2023). Existence and Uniqueness Solution of Certain Integral Equation. Academic Journal of Nawroz University, 12(4), 43–48. https://doi.org/10.25007/ajnu.v12n4a1978

Issue

Section

Articles